Radio frequency, microwave, and millimeter-wave integrated circuits are essential to the functionality of wireless communication, radar, and imaging systems. Integrated circuit design at these frequencies requires the use of on-chip passive electrical components such as resistors, inductors, capacitors, and transformers. Transformers and balanced-to-unbalanced (balun) devices are commonly used in wireless communications. A transformer is commonly used to couple differential radio-frequency, microwave, or millimeter-wave frequency signals between functional circuit blocks. Baluns are used for single-ended to differential conversion or differential to single-ended conversion of signals. The effectiveness of this conversion should be maximized in a useful balun design to maximize the signal power in the desired mode, for example in differential-mode.
In single-ended to differential conversion, with one port grounded on the primary coil of a transformer balun, the ideal output on the secondary coil would be purely differential. Suppression of common-mode signals at the secondary coil terminals is important to maximize the signal power in the differential mode, and also to avoid common-mode variation in the operating point of the subsequent circuitry.
At high frequencies, the parasitic capacitance between transformer windings leads to undesirable common-mode output at the secondary coil when the balun is excited with a single-ended input at the first terminal of the primary coil and the second terminal of the primary coil is grounded. The complex impedance of this capacitance becomes small at high frequencies, causing capacitive coupling between turns of each coil to itself, and also between turns of the primary coil to the secondary coil. The primary coil is asymmetrically grounded, but the secondary coil is uniformly coupled to the primary coil, causing a degraded common-mode rejection due to this asymmetry.
The differential mode conversion gain is the ratio of the differential signal power at the transformer secondary to the single-ended signal power at the first terminal of the primary coil, where the second terminal is grounded. The common mode conversion gain is defined similarly, but relates to common mode signal power at the transformer secondary. The common mode rejection of the balun is defined as the ratio of the differential mode conversion gain to the common mode conversion gain. Maximizing the common mode rejection ratio (CMRR) is desirable since it means more of the input signal power is being converted to the desirable differential output signal, and less to the undesirable common-mode output signal at the transformer secondary coil.